CA1154752A - Drill bit with dispersed cutter inserts - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
An earth boring drill bit has hard metal inserts in its cutter shells that are spaced to eliminate rows.
Each insert has a surrounding boundary zone with inner and outer loops corresponding to the minimum and maxi-mum desired distances between centerlines of inserts, respectively. Each insert has at least one insert lo-cated randomly in its boundary zone. In selecting the locations, a first insert is arbitrarily located. The location of a second insert is randomly selected within the boundary zone of the first insert. The location of a third insert is randomly located within the boundary zone of the second insert, so long as it does not come any closer to the first insert than the minimum desired distance between inserts. Each succeeding insert is chosen in this manner.

Description

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BACKGROUND OF THE INVENTION

1. Field of the Invention: This invention relates in general to earth boring drill bits, and in particular to the arrangement of the cutting elements.
~. Description of the Prior Art: The most common type of earth boring drill bits for oil and gas wells are cutters that rotate about an axis and roll around the bottom in a path or kerf as the bit rotates. The cut-ters have rows of tee~h that disintegrate the earth for-mation ~hrough force applied on the cutter. The teeth are spaced in rows and spaced to disintegrate as much of the bottom as possible in a single rotation. The prior art earth drilling bits include various features designed to avoid a problem known as "tracking". This problem arises when the spacing of the teeth on a ro-tatable cutter enables the teeth to fall repetitivelywithin previous tooth impreSSiGnS in the earth. Even-tually, ridges and peaks are formed in the earth, and as a result, the cutter experiences accelerated abrasive wear.
The teeth are thus worn prematurely and unevenly. In bits ~ith teeth of hard metal inserts retained by in-terference fit in drilled holes, the supporting metal may wear prematurely and the inserts may be lost.
Solutions to tracking are shown in U.S. Patent No.
3,726,350, R.C.O. Pessier, April 10, 1973, and in U. S.
patent No. 4,316,515, P~.C.O. Pessier, issued February 23, 1972. Another solution is suggested in U.S. Patent No. 4,187,922, F.E. Phelps, February 12, 1980.
In each of the above inventions, the inserts are ar-ranged in circumferential rows, with varying spacing among inserts to prevent tracking. These prior art inserts are arranged in groups, with similar spacing in a group, but differing spacing in other groups; or the spacing in each row progresses from a minimum ~o a maximum and back to the minimum; or the insert spacing is varied in each row so _3_ that each pair of inserts is separated by a space differ-ent from the space between all other pairs of inserts in the row.
In each of the prior art solutions discussed above, the inserts are arranged in circumferential rows. The rows are separated by a minimum spacing to provide ade-quate supporting metal for the inserts. To prevent the generation of a ridge between rows, another cutter posi-tioned in the same kerf or path may have staggered rows arranged to remove the earth where such ridges would otherwise form. Another method is to stagger the cutter itself from the other cutter in the kerf~ ,such as shown in U. S. patent No. 4~316~515~ RoC~O~ Pessier.
Occasionally, bits some-times rotate "off-center", meaning that the rotational axis of the bit becomes displaced during drilling from the central axis of the borehole. One result of this phenomenon is the generation of ridges, even between staggered rows of the various cutters.
There are regions of prior art cutters which have annular rows that overlap without intervening spaces.
In U. S. Patent No. 3,726,350, the cutter has half rows offset from each other. E. A. Morlan disclosed in U. S.
Patent 2,774,571, December 18, 19~6, the use of an in-ner end or "nose" of each cutter which has such an ar-rangement. J. H. Howard et al disclosed in U. S. Patent

2,230,569, February 4, 1941, a large number of arrange-ments for cutters with milled teeth, including helical rows of teeth. Also, shaft cutters with helical rows have been used in the prior art.
In all art known to applicant, the teeth or inserts are arranged in rows. The rows may be circumferen~ial and perpendicular to the cutter axis, or the inserts in the ~5~7~

row may only extend partially around ~he cutter. The rows may be parallel with the cutter axls, or the rows may be helical as menti.oned. All of the various arrange-ments, however, cannot completely eliminate tracking and provide full coverage in a single kerf with a single cutter.

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SUMMAR~ OF THE INVENTION
The object of this invention is to provide a drill bit for earth boring with cutters having inserts dis-persed over the cutter surface such that only one cutter may be used in a selected ker~, and providing more effi-cient rock fragmentation and balanced wear on the cut-ting elements.
Another object is to avoid tracking and eliminate ~-the generation of annular ridges, even during off-center running.
These objects are achie-ved in the preferred embodi-~ment ~y spacing the inserts in a dispersed pattern that eliminates rows and achieves widely varied spacing. To provide adequate strength of the metal supporting the inserts, a minimum distance is established around each 15 insert as one constraint on the insert spacing. To achieve an interaction between adJacent impressions on the borehole bottom, a maxlmum distance is established around each insert. The maximum distance is a function of the rock properties and the size of the inserts. Thus, 20 a boundary zone is established around each insert and in these zones the inserts are dispersed.
In choosing the ]ocation of the inserts in the pre-erred method, first an insert is arbitrarily located at any point within the selected region of the cutter shell.
~5 Then the location of the second insert is selected within the boundary zone surrounding the first insert by using in the preferred method a random number generator. The third insert is located in the same manner within the L
boundary æone surrounding the second insert. However, 30 the third insert may not be located closer to the first insert than the desired minimum distance between inserts.
The location of each succeeding insert is chosen in the same manner.

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BRIEF DESCRIPTION OF THE DRAWINGS
Fig. 1 is a frontal view partially in section of a raise drill reamer, having cutter assemblies constructed in accordance with this invention and shown in phantom as being rotated into the plane of the section to illustrate relative radial positions.
Fig. 2 is a schematic illustrating the insert posi-tions`of one of the intermediate cutters of Fig. 1.
Fig. 3 is a graph indicating the insert density of one of the intermediate cutters of Fig. 1.
Fig. 4 is a sectional view of a cutter shell for one of the intermediate cutters of Fig. 1.
Fig. 5 is a schematic illustration of a method of locating inserts in accordance with this invention.
Fig. 6 is a sectional view of a cutter shell for one of the inner cutters or gage cutters.
Fig. 7 is a schematic layout of-one of the rows of inserts in one of the gage cutters or inner cutters of Fig. 1. L.
Fig. 8 is a schematic layout of two of the rows of 20 inserts in one of the gage cutters or inner cutters of ~-Fig.`l.

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DESCRIPTION OF THE PREFERRED EMBODIMENT
Referring to Fig. 1, a raise drill bit or reamer 11 is shown boring a shaft 13, being drawn upward through a previously drilled pilot hole 15. Raise drill reamer 11 includes a cutter support member or plate 17 secured to be normal to a cylindrical stem 19. Stem 19 is secured to drill pipe (not shown) and has a longitudinal or ro-tational axis concentric with that of plate 17.
A plurality of cutter assemblies 21 are mounted to the plate 17 by cutter mounts 23. Each cutter mount 23 has two arms 25 spaced apart from each other and facing away from the cutter support plate 17. Arms 25 define ` a saddle or cradle for receiving a cutter assembly 21.
Cutter assemblies 21 include an inner cutter 27, several intermediate cutters 29, and several outer or gage cutters 31. Inner cutters 27 and the gage cutters 31 are preferably identical. Also, the cutting struc-ture of the inner cutters 27 and of the gage cutters 31 in the preferred embodiment is less than the width of the cutting structure of the intermediate cutters 29.
Each cutter assembly 21 comprises a cutter shell mounted on a bearing, $uch as shown in U.S. Patent No. 4,316,515, R.C.O. Pessier.
The cutter shell 33 for ~he intermediate cutters 29 is shown in section in Fig. 4. Each cutter shell 33 is generally conical and truncated perpendicular to rotational axis 35 to form a frusto-conical outer surface in roIling contact with the earth. Tlle inner side 37 of the cutter shell 33 is closer to stem 19 (Fig.
1~ and is smaller in outer diameter than the outer side 39.
Each cutter shell 33 has a nose region, an in~er-mediate region, and a gage region. Nose region 41 is an annular frusto-conical surface formed at the edge of in-ner side 37. ~he surface of nose region 41 is formed at an angle of fifty-four degrees with respect to axis 35.

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Gage region 43 is a frusto-conical surface formed a~ the edge of outer side 39. The surface oE gage region 43 is formed at an angle of sixty degrees with respect to axis 35. The intermediate region 45 includes an annular sec-tion 45a next to gage region 43 that is cylindrical and parallel with axis 35. A frust~-conical surface 45b joins sur~ace 45a, it being formed at seven and one-half ~egrees with respect to axis 35 in the preferred embodiment.
Another frusto-conical surface 45c, between surface 45b and nose region 41, is formed at a twelve and one-half degree angle with respect to axis 35. Mose and ga~e re-gions are defined herein to refer to surfaces immediately joining the inner side and outer sides, respectively, separated by the intermediate region and formed at sub-stantially greater angles with respect to the axis of rotation than the intermediate region.
Intermediate region 45 contains a plurality of holes 47 (only one shown) drilled normal to its surface for containing hard metal inserts 49 (Fig. 1), preferably constructed from sintered tungsten carbide. In the pre-ferred embodiment for intermediate cutters 29, there areno inserts located in the nose region 41 or heel region 43. The bottom hole pattern of the insert: holes 47 is shown schematically in Fig. 2, which represents the ap-pearance of the bottom of the boreholes ii- one cutter is rolled for one revolution. The left side of tlle drawing of Fig. 2 represents the inner side of the intermediate region 45, at ~.he intersection of surface 45c with the ` nose region 41. The right side of the drawing oE Fig. 2 represents the outer side of the intermediate region 45, at the intersection of surface 45a with gage region 43.
The inserts in the intermediate region 45 are dis-persed or irregularly located within the limits of bound-ary zones so as to eliminate circumferential rows. Each insert hole 47 in the intermediate region 45 has a bound-ary zone that surrounds the insert. The boundary æonefor a first selected hole 47' is shown schematically with w !

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-~3-dashed lines in Fig. 5 and consists of a first loop 53 corresponding to the minimum desired distance between centerlines of inser~s, and a second loop 55 correspond-ing to the maximum desired distance between the center-lines of inserts. In the preferred method and apparatus,the boundary zone loops 53, 55 are concentric circles and identical for each insert hole 47 located in the inter-media~te region 45.
The minimum distance is empirically determined by the necessary cutter shell metal needed to retain an insert. The maximum distance is determined by the ex-tent a typlcal earth formation is disturbed by a single insert. These minimum and maximum distances between ~-centerlines will also depend upon the cutter circumfer-ence, the insert shape and siæe, and the amount the in-sert protrudes from the cutter shell. In the preferred embodiment, for a cutter diameter of 13.496 inch at the inner side of intermediate region 45c, a diameter of 15.540 inch at the in~ermediate surface 45a, a hole 47 2a diameter of 0.6250 inch, and hole 47 depth of 0.500 inch, the minimum spacing between centerlines of inserts is 0.80~ inch. Thus the radius of loop 53 is 0.800 inch.
The maximum spacing between centerlines of inserts is l.350 inch for this cutter. Thus the radius of loop 25 55 is l.350 inch.
In the preferred method of selecting the location of the inserts, the location of the fi.rst hole 47' is arbitrarily selected at any point in the intermediate region ~5. Then, referring to the example of Fig. 5, the location of the centerline of a second hole 47" israndomly selected within the boundary zone loops 53 and 55 of the first hole ~7' as determined by a typical com-puter resident random number generator. The word "ran-dom" refers generally to an irregular selection that has no specific pattern within the specified boundary zones.

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Boundary zone inner loops 53' ancl 55' are then ap-plied around the centerline of the second insert 47", as indicated by the dotted lines in Fig. 5. The centerline of third hole 47"` is randomly located within the bound-ary zone of the second hole 47". However, the third hole 47"' may not be located closer to the first insert hole 47' than the desired minimum distance between inserts.
The portion of the boundary zone of the second hole 47"
that is too close to the first hole 47' is indicated by 10 the cross-hatched lines. This procedure is carried out witEI each succeeding insert location being randomly cho-sen within the boundary zone of the preceding insert, but c not closer to any previously selected insert than the de-sired minimum spacing between inserts. The procedure is 15 repeated until the intermediate region is completely cov-ered. Because of the space limits of the interme~iate region, there will be a few spaces that are greater than the desired maximum distance from inserts, but yet pro- _ vide insufficient space to place an additional inser-t 20 without being too close to an existing insert. The min- r~
imum distance must always be observed.
~he selection process can be performed manually or by a computer~ In the computer methocl, a random number generator is used to select the locations within bound-25 ary zone limits. In a pure mathematical sense, the pro-gram is not random since in a true random selection, re-peats will occur. The random number generator used with the program will generate approximately 50,000 numbers be-~ore repeating a number. This is sometimes called pseudo-30 random selection. The computer program in Fortran lan- L
guage is set forth at the end of the specification. In the program, the intermediate region 45 was assumed to be a single angle conical surface, rather than having multiple angles in the sections 45a, 45b and 45c.
35In selecting locations, certain of the insert holes 47 will fall close to the edge of the intermediate region ~`
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45. This is permissible so long as the cyli.ndrical sur-face of the hole 47 is no closer than about 1/64 inch from an edge of intermediate region 45. If the boundary zone of a preceding insert falls across an edge of the intermediate region 45, only the por~ion of the boundary zone inside the intermediate region may be used ~o locate an insert.
~he result is a cutter with an intermediate region 45 wherein rows are deliberately avoided. Preferably ~~
10 the spacing is dispersed such that there are no groups of three adjacent inserts wherein a single plane can be passed through the points where their centerlines inter-~sect the cutter surface. While i~ is possible for one or more groups to occur in the preferred method, such occur-15 rence is expected to be rare. Fig. 3 is a graph indicat-ing the approximate uniformity of coverage of the cutting structure. This graph has been prepared by starting at the nose region 41 and making a plot of the relative in-sert density as one proceeds outward to the gage region 20 43. The relative density represents the approximate total linear distance of inserts through which a selected plane passes, divided by the associated circumference of the cutter shell at the selected plane. The selected plane must be perpendicular to the axis 35 of the cutter shell 25 33. For example, a plane passing through the intermediate region 45c about one-half inch from nose region 41 and perpendicular to axis 35 would pass through a number of inserts 49. The plane might pass through and bisect some inserts while passing through only a segment of other 30 inserts. The distance that the plane cuts through each insert at a point flush with the cutter shell 33 is added.
When summed, these distances divided by the associated circumference yields about 0.2~ at a point one-half inch F
from nose region 41. If the inserts were spaced in a 35 circumferential row at this point, and had no cutter metal between them, then the relative density would be 1.0 or 100%., pp.

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Note that the coverage is fairly uniform, in that once past the first one quarter inch or so at both edges of the intermediate region 45, the clensity varies between about 0.15 and 0.28, and preferably does not drop below 0.10. This indicates that all possible planes passing perpendicular through the a~is 35 will pass through a portion o~ at least one insert. If there were circum-ferential rows, then the graph of Flg. 3 would register zeros between the rows, since the planes at these points 10 would fail to pass through any inserts.
Table No. 1, attached, lists the precise location of each insert 49 in the insert holes 47 in the inter-mediate region 45 for a cutter havîng dimensions de-scribed above. The column marked "A" represents the 15 distance along the axis 35 from the outer side 39 to ev the point where the insert is located. The angle ~ is a radial measurement of the cutter shell 33 about its axis 35, beginning with an arbitrary first point. The difference between any of the angles a is proportional 20 to the circumferential distance along the cutter's in-termediate region 45 in a plane perpendicular to the F
axis'35. Although not necessary to the invention, note that, to three decimal points, each insert: hole 47 is located at a different distance from the outer side 39 25 than all others. Also, each insert hole 47, to three decimal points, is located on a different radial plane than all other insert holes.
The insert locations were not selected by the com-puter in ~he numerical order shown in the table. That 30 is, the second i.nsert location chosen by the computer is not necessarily the insert number 2 in the table. Insert number 3 in the table is not within the boundary zone of insert number 2 in the table. Rather the table conven-iently lists the inserts by increasing angle ~ . The inserts numbered 292 through 294 are indicated in Fig. 3 to correlate Fig. 3 with the table. All of the insert ~`
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5 ~7 5 2 holes 47 are drilled normal to the surface that they are located on, except for holes that fall across the inter- :' section of intermediate region 45a with the intermediate region 45b, and the intersection of intermediate region 45b with intermediate region 45c. With these holes, the hole is drilled normal to the surface that contains more than half of the diameter. of the hole. ~~
~ igure 6 discloses a sectional view of an inner cut-ter 27 or a gage cutter 31 (Fig. '1), these cutters being identical to each other but considerably different from the'intermediate cutters 29. One reason is that the gage cutter 23 needs an extra high density of inserts on its ~outer edge for cutting the sidewall of the shaft 13. Also, the inner cutter 23 needs a row of inserts on its nose re- f'i' gion for cutting the edge of the pilot hole 15. For inter-changeability, the inner cutter 27 and gage cutter 31 are - made identical to each other, with rows of inserts being located both on the nose region and near the heel region.
The inner cutter 27 or gage cutter 31 comprises a cutter shell 53 that is generally conical and truncated perpendicular to its rotational axis 54. The bearings for the cutter shell 53 are of the same structure as used with intermediate cutters 29, Cutter shell 53 has an inner side 55 that is closer to stem 19 (Fig. 1~ than its outer side 57. Each cutter shell 53 has a nose re-gion, an intermediate region, and a gage region, as pre-viously defined,in connection with intermediate cutters 29. Nose region 59 is an annular frusto-conical surface formed at the edge of inner side 55 at an angle of thirty-five degrees with respect to the axis 54. Gage region 61is an annular frusto-conical surface formed at the edge of outer side 57 at an angle of sixty degrees with respect to axis 54. The intermediate region 63 includes an annular section 63a next to gage region 61 that is formed at an angle of five degrees with respect to a~is 54. A frusto-conical surface 63b joins surface 63a and is fcrmed at an angle of seven and one-half degrees with respect to axis f l~

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~i9L7S2 54. Another ~rusto-conical surface 63c, between nose re-gion 59 and surface 63~, is ~ormed at an an~le of twenty degrees with respect to axis 54.
Nose region 59 contains a row 65 of holes drilled and reamed for inserts 49 (Fig. 1). Row 65 contains thirty-seven holes, all spaced ~he same distance from the outer side 57. The pitch is defined herein to be the distance between centerlines of the inserts at the shell 53 surface. The pitch is varied in row 65 to a-void tracking in accordance witk the teachings in U.S.patent No. 4,316,515, R.C.O. Pessier.
Referring to Fig. 7, row 65 is divided into groups of increasing pitch, marked "I" and decreasing pitch, marked "D", in a counterclockwise di-rection. The pitch gradually increases in the increasing groups and gradually decreases in the decreasing groups.
The inserts marked with an asterisk fill in the space between the last insert in the last group in row 65 and the first insert in the first group.
The amount of increase in pitch, decrease in pitch and the number in each group are selected according to sever~l criteria. Firs~, there is a minimum pitch de-termined by the necessary cutter shell metal needed to hold the insert in place. The maximum amount of pitch is determined by the extent a typical earth forma~ion is disturbed by a single insert. This will be greater than the diameter of the insert 49 and depends also on the cutter she~l 53 circumference, and the size, shape and amount the insert protrudes from the cutter shell ~0 exterior.
The number of inserts within the group depends upon the desired change from insert to insert. To have an ap-preciable difference between the pitch from one insert to its adjacent inserts, generally groups from about three to seven inse~ts are used. To calculate the precise position, the number of spaces between inserts in tlle group, less one, is divided into ~he total increase in pitch. This i constant number is allotted to each space between inserts ;n the group. Consequently, in an increa~sing group, any space between insert centerlines will be the same as the preceding space in the group plus the constant number.
5 In a decreasing group, any space between insert center-lines will be the same as the preceding space less the constant number. Preferably the same maximum and mini-mum a~re used for each group within a single row.
Referring still to Fig. 7, row 65 has nine insert lO groups, five increasing and four decreasing. Two in-creasing groups are Eollowed by two clecreasing groups respectively. Each group contains five inserts, yield-ing four spaces between inserts in each group for vary- t ing pitch. Also, when an increasing group is followed 15 by a decreasing group, the groups overlap with the last ~, space of the increasing group being also the first space of the decreasing group.
Fig. 7 discloses the relative angular positions of the inserts in row 65, as indicated i.n the Table No. 2, 2Q set forth subsequently. Cutter shell 53 (Fig. 6) uses the same size of inserts 49 (Fig. 4) as cutter shell 33 F~
(Fig..4). However, it has different dimensions, it being 5.500 inches from inner side 55 to outer side 57, 15.601 inches in diameter at the inner edge of the gage region 61 and 14.262 inches in diameter at the outer eclge of the nose region 59. The angle ~ in Fig. 7 begins at zero with the ~ertical axis 67. The insert hole 65' located on the axis 67 is indicated in this table as insert tlO. 2, all of the inserts in row 65 ~or this particular cutter size being 5.219 inches from the outer side 57 as show~ in the "A"
column. The next insert hole 65" in row 65 is insert No. ~`
7 in Table No. 2, located 8.560 degrees rotationally from the centerline of the first insert hole 65' and from axis 67. The thircl insert hole 65"' is insert no. 13 in Table No. 2, located 17.940 degrees from axis 67 or 9.430 degrees from the centerline of insert hole 65".
The gradual increase and decrease in pitch and the Rs~

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insert locations can be determined through Table No. 2 in this manner. The other numbers listed in Table No. 2 disclose locations for other inserts on cutter shell 53, discussed subsequently.
Referring again to Fig. 6, a staggered row 69 of inserts is located in the intermediate region sec-tion 63b near the edge with intermediate section 63a. Fig. 8 is a layout similar to Fig. 7, disclosing the relative posi-tions of rows 69 and 71. ~11 of the insert centerlines of row 69 are located 1.874 inches from the outer side 57 while all of the insert centerlines of row 71 are located 1.581 inches from outer side 57. The centerlines are thus 0.~93 inches apart when measured along the axis 54. Since the diameter of the holes for these inserts is 0.625 inches, there will be overlapping coverage of approxi-mately one-half the insert's diameter. To assure some overlapping the axial distance between row 69 and 71 insert centerlines should not exceed the insert diameter.
The eighteen inserts of row 69 are divided in-to three groups of six inserts each. Each group of row 69 is a de-creasing pitch group, when considered counterclockwise.
The positioning of these inserts is selected as set forth in the discussion of row 65 and is set forth in Table No.
2. Each group of row 69 alternates and is circumferen-tially separated by a group of inserts frc,m row 71. Thefirst insert hole 69' of row 69 is listed as insert number 38 in Table No. 2, and is located 54.290 degrees from axis 73, which is the same axis as axis 67. The second insert hole 69" is listed as insert no. 46 as is located 63.430 degrees from axis 73.
The twenty-one insert holes of row 71 are divided into four groups, three of which have five inserts and one has six inserts. The groups of row 71 have uniform pitch between inserts. The first insert hole 71' of row 71 is listed in Table No. 2 as insert no. 5, located 4.940 degrees from axis 73. The second insert hole 71"

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of row 71 is listed in Table No. 2 as inser~ no. 12, located 14.810 degrees from axis 73.
Referring again to Fig. 6, a fourth row 75 of in- _ serts is located in the intermediate section 63a. The centerlines of all of insert holes of row 75 are spaced 1.015 inches from the outerside 57. There are forty insert holes in row 75 and they are divided into three increasing groups of seven inserts each or six spaces between inserts. Tle pitch of these groups is calculated as set forth in the discussion of row 65. Inserts are eqùally spaced between ~hese three goups. The precise positions are shown in Table No. 2, with all row 75 insert holes being found in the "A" column under the distance 1.015 inches.
Note, that for an insert of 0.625 inches diameter, the coverage of heel row 75 overlaps with the inserts of the staggered row 71 since they are only 0.566 axial inches apart. To allow this overlap, each insert of staggered row 71 is spaced between two inserts of heel row 75. The overlap prevents buildup between the heel ro~ 75 and staggered row 71. r-~ Referring to Fig. 6, a gage row 77 of gage inserts is located in the gage region 61. The gage inserts (not shown), differ from inserts 49 (Fig. 1) in that they have flat top surfaces. The gage inserts are mounted with their top surfaces flush with the gage region 61. Pref-erably there are thirty-nine equally spaced inserts in row 77, and these lnserts are not listed in Table No.2.
Referring to Fig. 6, a plurality of holes 79 (only one shown) are dispersed in the intermediate region sec-tions 63b and 63c. The locations for holes 79 are select-ed in the region between the nose region 59 and boundary zones of rows 69 and 71. Holes 79 are selected within the same maximum and minimum limits for the boundary zone as discussed in connection with the intermediate cutters 29.
The same computer program as previ.ously set forth is used for selecting the locations o.f holes 79, with different ~ j , , 7~2 numbers used for the dimensions of the intermediate re-gion. The locations of all o~ the randomly selec~ed in-serts in the cutter shell 53 are set forth in Table No. 2.
T~e numeral differences between the computer program for the ;ntermediate cutter shell 33 and t:he gage or in-ner cutter shell 53 are only in lines 00620, 00630, 006~0, 00650. The changes are as follows:
Line Shell 33 Shell 53 00620 7.074 7 ~73 00620 8.0?0 8.024 00640 9.893 11.0 ` 00650 5.506 2.~94 00~50 6.561 4.498 Also, lines 00660C through 00720C do not have the "C"
included in their designation.
Because of the irregular boundary provided by rows 69 and 71, there will be no circumferential space between rows 69 and 71 and the dispersed holes 79. That is, any plane passing perpendicular to the axis 54 in the inter-mediate region 63 will necessarily cut through a portion of at least one insert. Since the staggered rows 69 and 71 prevent any circumferential spaces to exist between these rows and heel row 75, there will be no spaces in the intermediate region 63 through which a perpendicular plane could pass without striking a portion of at least one insert. A circumferential space does exist in the nose region 59, inward from the nose row 65. The rela-tive density of inserts across the cutter shell 53 is fairly uniform, and preferably does not drop below 0.10, as previously defined in connection with cutter shell 33.
In operation, stem 19 (Fig. l) is rotated clockwise and urged upward. This causes cutter assemblies 21 to ~.

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L'752 rotate, creating an annular path about t:he borehole face 51. The inserts 49 disintegrate the earth, creating shaft 13.
The invention has significant advantages. In the in-termediate portion of the borehole, between the gage and inner cutters, only one cutter is required to cover an an-nular section of the borehole face, since the insert po-sitioning does not allow ridge buildup that might otherwise occur in the prior art between rows. Without the need for overlapping or staggering cutters, greater pressure can be exerted through the inserts, since there will be fewer cut-ters for transmitting the force imposed on the bit. Fewer cutters reduce maintenance required in shaft drilling. The shaft face is evenly covered, providing efficient fragmen-tation and avoiding uncut bottom due to off-center running conditions~ Since overlapping cutters are not required in the intermediate portion, tracking between cutters is avoid-ed.
The combination of the dispersed pattern with rows of inserts with varying pitch for the gage and inner cutters evenly covers the borehole face. The rows provide higher carbi`de density for the pilot hole and sidewall areas of the borehole. The varying pitch in these rows avoids tracking.
While the invention has been shown in only one of its forms, it should be apparent that it is not so limited, but is susceptible to various modifications and changes without departing from the spirit thereof.
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J6 19.18b 6.289 57 70.J15 4.702 17 19.422 4.576 ~5fl 71.737 2.096 18 2 ~ .17(~ L .864 59 75.719 1. ',3', __ _ 19 22. g 6 ~, ¦ 7 () 8 6 ()76. () L 4 '" 16 L L
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21~ S .827 3.95 () h 176. n 7 '. 5.800 21 25. f37 U ~ . f3 f37 6277. L ~1 1 2. ~,35 , 29.~2~ 1 217 6 3 77.',30 tj.()28 23 30.19~ ~.()()f. ~4f~0.~;3() 6.461 24 3U.~5; 2.4] ? Cr) 8(1.5f9 2.]?1 ._ .
2~ 3 .1f34 1. '. (. fl6I . ~)(,, 1. ()63 26 32. ', ~ ~, 42 c~ ',731. ? 53 3.44 27 32.505 ' .111 r7f~~32.() ,1~ 4.ll2 ~ _, 2~3 35.~() 2.7~35 69 8~.7(-1 , .7l() . _ . ......
29 35.9~3;. , .6 ~ ~ _ 70f~7.51 ~) I .3~() 37.475 3.613 7J f37.G37 4.888 31 37.591 1.849 72 87.891 2.5 ?7 _ __ _~___ _ 32 38.839 ~.072 _ 73 ~9 0~() ,4-1 33 39.066 4.410 74 90.031 3.?.74 . _ _ ,.
34 41.853 2.~103 75 9L?.552 6.29', .._ ._ 3542.694 fj.l97 7~, Y .9'5 1.041 J~,43.273 5.232 ~~ 77 93.(~1lJ 5. '~S
346.! 43 I . h 31 7~3 95.5S6 1.994 :~t3 ~ 7. 35U -3 ~( l, ~ 7g 95.9~6 4. ',26 ~ ~ r -~c~ t ~ 8 ~ j :, . f S I 80 ~ 07 2 922 - :- -- ~ __ _ ~ _ - --~_ ,~ 1 _ _ 1 2 I 1 ll 8. ',9 /~ 3.1 '34 8] ~ 9.53~ ( . ~ ______ ~
. .
I ~'~ I '~ .7'~) ~" 7'J~
8 ' 9 (~ .7 ~ ~' 'j .3 '31 ___ I ~ :~ 1 j ] 59f. l . '~ 7 ~3 83 101 9()4 ].~91 _ _ . __ 1-24 I')1.~355 2.4~S
8S 102.276 2.039 12'i 154.56(~ 3.769 103.43 ' 3.5 'j 7 ______ 12~ ~ 54.59'2 1 'J53 86 104.270 ll. i8n ______ 127 157 4n8 6.105 87 108.129 3.02'~ __ ______ 128 1 S7.8/ln 3. n84 88 108.255 l .701 ______ _ 129 15~3.~66 4. ~6'3 89 108.354 5.835 _ ~
130 160.213 1.85G
111.146 1 3.968 _ 91 112.865 5.0~5 I3] _ 160.267 _ 1.056 92 113.4~` (~.4~4 13;' 16().727 '3.96]
93 ~14.497 2.999 1'33 164.258 5.831 94 116.327 2.~05_ 134 164 671 _ 4.7/~3 ~ t 116.353 1.403 ~ 35 1(~6.019 1.48~
l '36 166 U`J 2 ~ R l 4 96 ] 17.798 4.25l _ _ . . r 97 11B.02' ` S .668 1:37 163 348 'I .842 9~3 12'1.284 3.455 138 1 `~U 730 5.196 99 121.914 '4. R96 1 '39 173.285 2.211 lC0 122 057 1.286- I~.~ 17~.5~l~ '3.2~9 01 123.157 6-.427 ' 14l J7'3.921 6.l;4 _ 10~ 125 587 - ' 2.28-~ 1/.2 17/.762___ 4.289 r _ ] ~ 1 175.55~ ] 29 103 126.'509 4.073 __ .
104 128.166 5.~22 1~' 177.134 ').~ 30 105 128.441 1.463 '~ 145 179.328 2.~ 0/~
106 131.087 3.182 146 119.995 6.442 . _ I1~7 180.189 3 ~6 107 131.15() ~ 01 __ . ~
_ 148 181.2 '36 1.0~ 8 1~)~ 133 733 6 412 _____~ ~ ______________ . 149 ] 8~ .58~3 4. ~80 109 134 106 ' 1.129 ______ ~ _____________ _ _ 15() 184.897 ~ .667 110 134.464 5.578 - _ ~__ __ __, ___ - - - _ _ 151 185.716 5.566 111 135.683 2.215 ______ ~
______ _ _ _ 152 186.530 6.389 112 136.234 3.7~0 ~ __ _ _ _____________ ~ 5 '3 187.729 2.801 113 138.749 4.50~ ______ ~ _____________ 154 1~9.803 3.8'36 ~r 114 139.945 3.112 _ . ~ _~
1~5 1(~2.064 S.113 115 141.179 1.6~(~ ______ ~ ___ __ _ _ l S" 192. ~S 1.9~6 116 142 368 ' 5.'352 _ . __ _ _ _ ] ' 7 1 '~2.17S 3.112 117 142.952 6.ll2~ _ _____________ _ _ _ 1 S.~ ~ 95.765 5.992 118 144.681 3.9~ ~ ~_____ LS~ I'J5~83l 3 307 119 145.3~2 ~ .207 _ _ . F' _1~,0 196 134 '~ ~55 ~120 348.l~62 1.'3~.3 - __ r~ . ......... _ .. 2~ 75Z
`_ _ =__ _ 'I 1,~',_O. 1 I t)I l'~f~.~f~ `~ ' J7 1 _ _ ,,~("~ ("421 .
,~() 2 ~)'ll) t~ 2 ¦ 9 ~) ~ ) 5 , _ _ _ 1 t 3 ; 99.71 :3 ,` t~ ~ (J ___ _ _ _ f~ ) . __ I 64 ~ ( ) 2. b 2 I /, . :~.1 . ( ) ~ ~ ~ `4 Y . l fG ') 3.72 f 3 _ .~
1 b 5 2 O 4.354 I .818___ 2 / '),47 ') 5.257 1 ~.6 20! .759 (~ 37 S.` (I fj ? 51.746 I .128 . .
!b7 207.()2~ 3. ' ;'~ _ ')~ ;'54.~)69 ).()Sf~
1~ 8 207.179 'i . I h 5 / ) q 2 5 I .6 / 4 4.2 G 3 I f.9 2 O 8. l f.8 2.6 ~ 9 ) J 255. (!/ ? 6. I 4 170 ? () i~ .272 ~ . ( ) 8 :3 ~ ~ __ _ 1. g iS~ (J
71 21 I .294 6 . I)9 3 ~ I i ~ ~. . sn,~ , . 33 I
72 213.234 3.1~4 ,1~ _'-'1,21~ 3.~Ui 73 213.906 S . l 69 ~ I I ~5~ . 2()/
~74 213,9~f~) 3.9i~1f~-- _ 14 2f~().if)f) ~ 95 17~ 213.951 I .663 1) 1 ', )l) I . '.()`~ 'i, 'J4(, 176 2 I f~) .771 ' . b 7 4 ~ 2 h l . i~33 'J / . 351 77 !]9.103 I ,0')1 .`I 7 2f-5.(~] I 1. /21 yr ~7i~1 `1~).3f~ 4.-527 ~ ~t)l~.4'1) 2.f~
! 7 q ? 1 ~ .4 '~ 1 5, 6 0 b _ ~ ! (J .I () f` !~ 6 ~ -'2(). b l~, I . '-66 ,';'l~ Lf ~.0' U (~. ()qfj I fJ 1 2 21.733 _ ' ,' I ' 6 f1; 'j ,~ ~ _---I ~- '' ! 2 ' . 3 ? 2 S . 1 f 4 I ~ ,~ ? 6 '3 . 1 ~' 3 3.597 If31 ;'2').4~3 4,305 ?7 3 '. l56 I ~:`, q, ~ ? .7 :~ 7 .' `, ,) ~ ~ o ~ /, ~ . S ~) 6 I f35 2) / .34] (' .1 ()5 .' ' 5 27 '~,1 (17 ___ _ ~t) ' ' f~,9 f~() 1, b 94 . ~ ~ 75 ~ 6f~ 5 3 n I s i~37 qq() .899 7 __ 2 ' 7 ;~ 77 . ~6 ) . 052 ~ !df~ ~ 3() ~ 958 4 . 7 9 b ... 177. fl/. I 6 . I~4 1 1 ~i 3 L 3.` ,054 . , f 3 `16 ) 27 J .129 ;~ ,2 .` ~ (! 2 i 't .49 ;2 3.831 33.387 ` .()75 _~ ~ ~ ___o_ , _ _ _ _ _ 7 11 ~f; 1.7 ~ I I ()6 1~1 2 ~3.723 5.942 ~ ~ _ _ ~ :~,.' ~f~ )2/~ ~ l) 1'32 2~3b.159 4.103 _ ~ ___ .'~ A~f~ y) () 3fjl 193 23b.676 1.073 _ ~ ,_ _ ~ _ ___ ~ ~ !, , ~16, f~ ~ 1 S .; '~
194 q 37.128 1.296_ _ __ _ _ ~ `flfj,9('~1 4.
13 S L 37.445 S .153 ~ ~ f, ~liii~- 2 1 S~ 6 2 !1 0 . 8 L 5 ) . S ? 1 .
i97 `41. '10---- f,),4 38 ~ ~7 ;'1)l . 31)U I .U')~
.__ ~ ~ 38() 2 '~
~1 f3 L 4 1 . f~ 7 5 I ~ 5 L 6 ___.__ r~
__ 7~q 1`(12 5~2 S ~'30 ~9~ 243.0l~3 5.579 ,_ _ _ -~ 9F
` O-' 2 4 3 . ~ ~ 7 3, 2 13 ? .~1/ ) ? '`~ '., 0 / 7 _ - _. _. _ . . . , _, . . .

~ -- - - -23~ 75~

_ _ T~L~ M(). 1 24~ 294.542 - 2.227 __ 730 ;~ 2.l 48 - -2C 2 295.964 3.76(. 28~ 3~ 4.643 4.023 _ _ j. . . . .___ 243 298.867 1.180 282 3/ 6.415 5.099 . _ . _ . .. ..
244 300 366 4.822 283 ~46.658 I.559 ~45 300.779 S .707 284 3~ i.-3-~4 -- 6.076 . ` _ 246 30l 7ao 2.72~ 285 3 7. ~ 93 2 ~ 01 24~ 303.590 1.855 2~35 34~.~313 3.~57_ . ._ ~- .
248 3n~.609 1 7l9 287 35l.194 4.21 _ . ~ _ ~ . . ~
243 305.979 1.102 2~8 :35~.5/6 2.543 250 307.224 6.4~4 289 3 ~ 3.593 5.100 ._ . ___ 11 251 3~8.434 5. ~22 2~0 3~4.036 5.361 __ _ ..... _ . 11 252 308.552 3.129 291 354.275 I.fi53 ~ .. ... . ___ 253 308.800 4.414 292 357.772 3.395 ._ . . . . .-- .
254 309.961 2.272 ~93 358.809 4.5~ 2 255 312.821 1.581 ~29~. 359.549 - 1.0~3l ----- -. _ 256 315.905 3.903 257 316.163 3.078 .
258 /~ 5.172 259 317.126 6.132 260 318.283 2.074 261 318.994 1.198 _ 262 3~2.3~4 2. fi85 2~3 323.195 4.104 264 324.405 1.578 265 325.035 6.305 _ 266 327.417 5.273 267 327.625 3.5~4 2~8 329.556 1.060 329.768 2. ~fiO
_ ~
27n 33l .292 4.655 . ~, 271 331.871 6. ~57 27~ 333.889 1.639 273 335.23~ 3.53~3 ~74 335.820 2.670 _ _ _ 2 ~S 336.249 5.696 . . ..... .
276 337.643 4 580 . __ 277 338.635 6.437 _ 78 339.228 1.310 ~79 341.522 3.314 ..

~ _ _ 7.5;~

CCMPUl'ER Pi~O&RAM
00120 C INPUT TO l~E PRO~RAM ARE (IN CONSISI~NT UNIl'S~
00130 C Rl=INNER CONE RADIUS AT TIP OF CCMPACT
00140 C R2=OUTER CONE RADIUS AT TIP OF CCMPACT
00150 C NC~hY=~Y. Nl~ER OF CCMPACI'S INCLUDING PREFIXED CO~PACrS ~-00160 C NC~DN=MIN. NUMBF.R OF CCMPACTS INCLUDING PREFIXFD CCMPACTS
00170 C DM~Y=MAXIML~I COMPACT SPACIN& TIP TO TIP
00180 C rMlN=MINDMMM COMPACT SPACING TIP TO TIP
OGl90 C N=NUMBER OF PREFLYED C~MPACTS ON INNER AND OUTER RoW ONLY
00200 C D=COMPACT DIA~I~R
00210 C H=COMPACT HEIGHT
00220 C FSEED=STARTIN& "SEED" FOR RANDoM NUMBER &ENERATION
00230 C NCl=NUMBER OF PREFLYED COMP~CI~. ON INNF,R R~W
0024~ C NC2=NUMBER OF PREFLXED CCMPACTS ON OUTER P~W
00250 C THETA=CONE AN&LE IN DEGREES (NOT INCLUDED) 00260 C PI,TOPI=3.1415927,6.2831854 00270 C WIDTH-CONE LENGTH ALONG GENERATOR LINE FIRST TO LAST CCMPACT RoW
00280 C TOI~D=CONE LENGTH ~ ONG GFNFJRATOR LINF. FIRST RCW TO RACKFACF, 00290 C ALPHA(I)--ANGLF,S OF PREFLYED COMPACTS ON INNER AND OUTER
00300 C RoW IN DEGRE,F.S STARTING WITH INNFR R~W
00310 C BETA(I)--ANGLES OF ADDITIONAL PREFIXED COMPACTS IN DEGREES
00320 C RBETA(I)-`RAD~L POSITION OF COMPACTS AT T~E TIP
00330 C NMORE=NUMBER OF ADDITIONAL PREFIXED C~MPACTS ~-00340 C $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
00350 C IF NO RCWS OF CCiMPACTS ARE PREFIXED, THE PRC~E~M MAKF,S A RANDOM
00360 C S~ FCTION OF THE FIRST CCiMPACT. THE RANDOM NUMBERS ARE GENERATED
00370 C BY THE USE OF lHE M~,TIPLICATIVE LINEAR CONGRUENl`IAL MElHOD:
00380 C U(N~lj=FRACTIONAL PART OF 997-~''U(N). U(l) IS CALLED SEED. THE
00390 C PRC~RAM ASSUMF.S .5284163 AS SEED (ALTHOUGII ~THER APPROPRIATE
00400 C SEEDS MAY BE USED). T~E PERIOD OF l~E GENFRATOR USING THIS SEED
00410 C HAS A LENGTH OF 500,000 NUMBERS. THIS IS USING 10 M GITS
00420 C CALCULATIONS. T~5E M~ST SIGNIFICANr DIGITS (THE LEFT HAND M GITS) ~-00430 C ~RE THE ~ST RANDOM DIGITS.
00440 C $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
00450 C OUTPUr FROM T~E PROGRAM ARE:
00460 C N=COMPACT COUNTER
00470 C RHO(N)=RADIAL COMPACT POSITION AT ~ E TIP
00480 C ALPHA(N)=ANGULAR COMPACT POSITION IN DEGRE~S
00490 C M ST(N)=DISTAN OE CENTER OF CARBIDE HOLF. ~ro BACKFAOE
00500 C Y(N),X(N)=COMPACT COORDI~l`ES FOR PLOITER
00510 C` $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$~$$$$$$$
00520 C THIS PRDGRMM ALSO C~LCUTATES THE CARBIDE DENSIlY ACROSS THE
00530 C SURFA OE OF T~E CONE SHELL AND STORF.S THE DATA IN THE SAME ~ATA
00540 C SET (PACCA.DATA) FOR USE BY T~IE PLOTTING PROG~AM "UNIVPLTC" T~
00550 C PLOT BOrH COMPACT LOCATIONS AND CARBIDE DENSITY.
00560 C --00--00--00--00--oo--oo--oo oo oo oo oo--oo--oo--oo--oo-00590 IMPLICIT REAL*8(A-II,O-Z) 00600 DIMENSION Y(500),ALPHA(500),~HO(500),DX(500),XS(500),YC(500) P-00610 DIMENSION XD(500),YD(500),1HI(13),BETA(300),RBE~A(300) 00620 DATA Rl,R2,NCMAX,NCMlN,DMAX,DMIN,N,D,H,FSF~D/7.074,8.020,395, 00630 169,1 .~50,0 800,O, 625, 750 52~41~3/
00640 DATA NCl,NC2,THETA;PI,TOPI ~b,0,9.893,3.1415927,6.2831854/
00650 DATA WIDIH,TChlD,N~lORE/2.84,4.98,1/ 5.506,6.561,0/
00660 C DATA BETA/54.29,63.43,71.84,79.52,86.47,92.69,151 91,161.05, 00670 C C169.46,177.14,18'~.n9,190.~l,249~3,258.67,267.08,274.76,281.71, ~475~

00680 C C287.93,282`'`-0.DO/
00690 C n~TA RBF.TA/18*7.967DO,282`''0.DO/ , 00700 C DATA AlE~l4.94,14.81,24.68,34:55,44.42,l02.56,112.43,122.30, 00710 C C132.17,142.04,200.18,210.05,219.92,229.79,239.66,297.80,307.67, 00720 C C317.54,327.41,337.28,347.15,479`''0.~0/
00730 C DATA ALP~0.0,7.14,15.12,23.93,33.59,44.08,51.22, 00740 C C59.2,68.01,77.67,88.16,97.82,106.63,114.61,121.75,132.2~ 1.9, 00750 C C150,71,158.69,165.83,172,97,180.95,189.76,].99.42,209.91,217.05, 00760 C C255.03,233.84,243.5,253.99,263.65,272.~6,280.4~,287.58,298.07, 00770 C C307.73,316.54,324.52,331~66,340.~7,350.13, 00780 C C.200.0,206.22,213.17, 00790 C C220.85~229.26~238.4~244.62~251.57~259.25~267.66~276.8~285.21~
00800 C C292.89,299.84,306.06,315.2,323.61,331.29,33~3.24,344.46,350.68, r-00810 C C357.63,5.31,13.72,22.86,29.08,36.03,43.71,52.12,61.26,69.67, 00820 C C77.35,84.3,90.52,99.66,108.07,115.75,122.7,:l28.92,135.1~,142.09, 00830 C C149.77,~58.18,167.32,175.0,183.41,192.55,412~0.DO/
00840 DATA IHI/'R.M.','I. ','6/05','/79 ',' 3"',' CUT','TER ','343', 00850 C'COMP','ACTS','--NO',' RCW','S '/
00860 ~RITE(6,200) 00870 200 FORMAT(////,1~X,'N',16X,'RHO(N)',lOX,'AIE~(N)'jlOX,'DIST(N)', 00880 C9X,'Y(N)',14X,'X(N) 00890 CON=PI/180.
00900 I~ETA=IHETA*OON
00910 ZROT=PI~';DSIN(T~EIA) 00920 RM=Rl-.25`~`L`cos(THETA)-~TowI~l;DsIN(T~ETA) 00940 WRITE(2,307)ZROT,R1,R2,PI,IHETA,D
00950 307 FORMAT(6F12.7) 00960 ~RITE(2,318)IHI
00970 318 FOR~T~13A4) ~_ 00980 IF(N.EQØAND.NMORE.EQ.0) GO TO 15 00990 .IF(N.EQ.0) GO TO 12 01000 DO 1 I=1,N
01010 ALFHA(I)=AIPHA(I)~'CON

01030 IF(NC1.EQ.0) GO TO 6 01040 RH=R1-.25'''DCOS(T~ETA) 01050 DO 5 I=1,NC1 01060 DX(I)=(RM-RH)/DI~N(TI~ETA) 01070 R~IO(I)=Rl 01080 CALL POS(Rl,THETA,CON,AIPHA(I),ZROT,ZETA,Y(I),XS(I),YC(I),ANGLE) 01090 WRITE(6,250)I,Rl,ANGLE,DX(I),YC(I),XS(I) 01110 IF(NC2.EQ.0) GO TO 11 01120 6 NCS~NC1+1 01130 KH=R2-.25`;L~OS(THETA) 01140 DO 10 I=NCSUM,N
01150 RHO(I)=R2 01160 DX(I)=(RM-RH)/DTAN(T~.TA) 01170 CALL POS(R2,T~ETA,CON,ALPHA(I),ZROT, ÆTA,Y(I),XS(I),YC(I),ANGLE) 01180 WRITE(6,250)I,R2,A~GLE,DX(I),YC(I),XS(I) 01200 11 IF(NMDRE.EQ.0) GO TO 16 01210 12 DO 99 I=].,N~RE
01220 BETA(I)=BF.TA(I)~''CON

01240 IIN=N~1 ` Fr ~5~'7~

01250 IFIN=N~NM~RE
01260 DO 13 I=IIN,IFIN
01270 ALPHA(I)=BETA(I-N) 01280 RHO(I)=RBETA(I-N) 01290 RH=RHO(I)-.25~DCOS(TÆ TA) 01300 DX(I)=(RM-RH)/~T~N(THETA) 01310 R=RHO(I) 01320 CALL POS(R,TÆ TA,CON,ALPHA(I),ZROT,ZETA,Y(I),XS(I),YC(I),ANGLE) 01330 WRITE(6,250)I,RHO(I),ANGLE,DX(I),YC(I),XS(I) 01350 ~N+~MORE
01360 GO TO 16 ~_ 01370 15 N=l 01380 RAN~ANY(FS~D) 01400 RHO(N)=RA~nr`;(R2-Rl)+Rl 01410 RH=RIIO(N)-.25`';DCOS(THETA) 01420 DX(N)=(RM-RH)/DrAN(n ETA) 01430 RAND=ANY(FSFED) 01450 ALPHA(N)-RA~n~ TOPI ~, 01460 R=RHO(N) 01470 CALL POS(R,THETA,CON,A ~ ~A(N),ZROT,ZErA,Y(N),XS(N),YC(N),ANGLE) 01480 WRITE(6,250)N,RHO(N),ANGLE,DX(N),YC(N),X~S(N) 01490 16 DAM~=~MAX/Rl 01500 KN=O
01510 18 DO 60 Kl=l,N
01520 RAND=ANY(FSEED) 01530 ADIST-RAN~(DMAX-DMIN)~ IN
01540 FSEEL=RAND
01550 KTIME=50 01560 ~O 40 J=1,100 01570 KTIME=KTI~E+l 01580 IF(KTIME.LT.100) GO TO 20 01590 CALL TI~ER(KII~E) 01600 KTI~E=0 01610 20 r~l.0 01620 ICOUNr=0 01630 KKK=0 01640 RANDtANY(FS~Fn) 01650 AKT=RA~'~OP.I
01660 FSEED=RAND
01670 IF(A~r.LT.PI) GO TO 21 01680 KKK=l 01690 AKT=TOPI-AKT
01700 21 SINE=DSQRT(Y(Kl)'W'2+ADIST~'~2-2.~Y(Kl)~ DlST`~'`lX~OS(AK~')) 01710 IF(A~r~E~ pI~oR AKT~EQ~o~o~oR~AKT~EQKropI) DAN=0.0 01720 IF(DAN.EQØ0) C~ TO 27 ~_ 01730 IFCY(Kl).NE.SINE) GO TO 24 01740 23 ETA=PI-2.`'AKT

01760 24 ETA=DARSIN(ADIST'~DSIN(AKT)/SINE) 01770 26 DAN=ErrA/DSIN(THETA) 01780 IF(DAN.~r.DAMA) CO TO 40 01790 27 RAr~SL~ 'DSIN(I~ErA) 01800 IF(NCl.EQØAND.NC2.EQ.0) GO ro 30 F

7S;i~

01810 IF(NCl.EQ.0) GO TO 28 01820 IF(NC2.EQ.0) GO TO 29 01830 28 IF(RAD.LT.Rl.OR.RAD.OE .R2) GO TO 40 01850 29 IF(RAD.LE.Rl.OR.RAD.GT.R2) GO TO 40 01870 30 IF(RAD.LT.Rl.OR.RAD.GT.R2) GO TO 40 01880 31 IF (KKK)32,32,33 01890 32 ANGLE=ALPHA(Kl)-DAN
01900 IF(ANGLE.LEØ0)ANGLE=TOPI+ANGLE

01920 33 ANGLE--ALPHA(Kl)+DAN
01930 IF(ANGLE.GT.TOPI)ANGLE=ANGLE-TOPI
01940 34 DO 35 K2=l,N
01950 DIST=R Wr(ALPHA(1~2),ANGLE,Y(K2),SINF.,PI,TOPI,THElA) 01960 IF (DIST.LT.DMIN) GO TO 40 01970 IF(DIST.GE.DMIN.AND.M ST.LE.DMAX)ICOUNT--ICOU~r+l 01980 35 CONTINUE t-01990 IF(N.EQ.l) G0 TO 37 02000 36 IF(ICOUNT.LT.2) GO TO 40 02010 37 N-N+l 02020 Y(N)=SINE
02030 RHO(N)=RAD
02040 RH=RHO(N)-.25`~'DCOS(THETA) 02050 DX(N)=(RM-RH)/D~AN(THETA) 02060 AIE~A(N)=ANGLE
02070 Z~TA=ANGLE~`DSIN(I~ETA) 02080 XS(N)=SINE`~`DSIN(ZETA-ZRDT) 02090 YC(N)=SINE''`DCOS(ZETA-ZROT) 02100 ANGLE--ANGLE'`~180./PI
02110 WRITE(6,250)N,RAD,ANGLE,DX(N),YC(N),XS(N) ~-02120 250 ~OR~AT(lOX,I5,15X,F6.3,10X,F8.3,10X,F6.3,10X,F6.3,10X,F8.3) 02160 IF(N.GE.NCM~uY) G0 TO 70 02170 IF(N.LE.NCMIN) GO TO 18 02180 IDIFF=N-KN
02190 IF(IDIFF.EQ.0) GO TO 70 02200 KN=N

02220 70 WRITE(2,327)N
02230 327 FOR~T(I5) 022~0 L=N-l 02250 75 DO 76 IS=l,L
02260 J=IS-H
02270 IF(A ~ ~A~IS).LE.ALE~IA(J)) GO TO 76 02280 A=AIEHA(IS) ,~
02290 B=DX(IS) 02300 ALPHA(IS)--A~HA(J) 02310 DX(IS)=DX(J) 02320 AIPHA(J)=A
02330 DY(J)=B

02360 ~RITE(6,330) r 02370 330 FoRMAT(35(l)~2ox~N~llx~ALpHA(N)~7x~DIsT(N)~) ~ , . .

5~L75~
2~ _.
02380 DO 77 IST=1,N
02390 ALPHA(IST)=AI.PIIA(IST)/CON
02400 1~RITE(6,335)IST,ALPHA(IS'r),DX(IST) 02410 335 FORMAT(16X,I5,9X,F8.3,10X,F6.3) 02420 77 CONTIN~E
02430 `DO 80 I=1,N
02440 ~RITE(2,396)XS(I),YC(I) 02450 396 EORMAT(2F15.7) 02470 ~WqDTH+~+.1 02480 ND=1~/.1 02490 WRITE(2,440)W,ND ~_ 02500 440 FORMAT(F15.7,I5) 02510 B1=(Rl-.25~';DCOS(THETA))/DSIN(THErA)-D/2.
02520 B=B1 02530 DO 95 JD=1,ND
02540 C~LL TDMER(100) 02550 SUM~-0.0 02560 DO 90 l~L=1,N
02570 YUP-Y(KL)-.25/DTAN(THETA)+D/2.
02580 YLCW'-Y(KL)-.25/DIAN(T~TA)-D/2.
02590 IF(B.LE.YLOW.OR.B.GE.YUP) GO TO 90 02600 T=B-Y(KL)+.25/DTAN(THETA) 02610 C=D-2.`''DABS(T) 02620 SUM=SU~C

02640 XD(JD)=B-B1 02650 YD(JD)=(SUMV(TOPI'''B'''DSIN(THETA)))`l'10.0 02660 B=B+.1 02670 1~RITE(2,396)XD(JD),YD(JD) r 02690 ~TOP

02710 FUNClION ANY(FSEED) 02720 I~LICIT RE~L`~8(A-H,O-Z) 02730 RAN=997.`~`FSEED
02740 M~RAN
02750 ANY=RAN-FLOAT~
02760 RETll~N

02780 SUBROUTINE POS(R,THETA,CON,ALPHA,ZROT,ZETA,YjXS,YC,ANGLE) 02790 IMPLICIT RE~L*8(A-H,0-Z) 02800 Y--R/DSIN(THETA) 02810 ZETA=ALPI~A'~`DSIN(THETA) L
02820 XS--Y~"DSIN(ZETA-ZROT) 02830 YC--Y~`DCOS(ZETA-ZROT) ~-02840 ANGLE=ALEHA~CON
02850 RE~RN

02870 FUNCTION ROOT(ALE~lA,ANGLE,Y,SlNE,PI,'1~PI,1~-D~r~) 02880 IMPLICIT REAL*8(A-H,O-Z) 02890 PHALA=ALPHA
0290Q GLANE=ANGLE
02910 IF(DABS(PI~ALA-GLANE).LE.PI) GO TO 10 02920 IF(PHAlA.GT.PI) PHAIA=PHALA-TOPI
02930 IF(GLANE.GT.PI) GLANE.-GLANE-TOPI
02940 10 UNA=DBS(GLANE-PHAIA) .

5~7~

02950 UNA--UNA`~'`DSIN (THErA~
02960 R~I)SQRI (Y`~2+SI~;'`~2- 2 . '''Y~`-SINE;'''DCOS (UNA) ) 02970 R~'TURN

READY

, 2 -`
_ -30-___ TABLE N0. 2 _ ~ .. ~ __ _ _ o N0 oC + .02 A + 015 _ _ __ 1 0,000 1,0] 5 23 3~.62~) 3./196 I __ 2 0.000 5.219 2'l 3~s-55() I.5~31 _ I _ 3~ ()7 ~.6~2 3 1.641 40413 __ . __ ___. L.
4 ~3.5233.651 _26 _ _ 39.13() __ _ 5 - Z19_ _ . . . _. ____ 14 9401 581 27 39.303 2.()23 r ~ . . . ._ __ ~ _ _ _ _

6 6.505 2.814 28 39.480 1.01S
~ __. _.__

7 8.560 5.219 29 39.520 4.414 ' r : . .. __ ____. _ __ __ _.. ._.__

8 9.870 1.015 30 ~0.567 2 967 .__ ____ ___..... _._. _ _._ _ .

9 11.714 4.131 __ ___ _ 4l~.~20 1.58 _ 11.727 2.399 32 46.61i 7 3.4~ ~
_ _ ___ __ ___ _ _____.__ _ _ 1-1 13.983_ _3.31_ 33 l7.690 502l9 12 14.8]01.581 34 L 4~.-338 4.271 _ ___.______ __ . ___ _ .__ __ 13 `17.94~5.219 ~5 ~.(34~ 2.65~
, . __ .. ._._ _ ~____ _. ___._ _ ___ __ _ __ .
14 19.740 1.015 1 3~ 49.350 1. Ul j _ ._ . _. . _. _._ ___ . . .. . _ _. ___ ___ ~ 15 19.827 4.030 _ _ _ _ _ _ ; __ _ _ i 3n 5l~ .29n ] . ~7~l 16 120.261 2.377 _ __ _ __ _____ __ __ ___ ___ 17 123.781 3.239 ___ _ 54. gOS 3.0~7 _ I
18 24.680 1.581 40 55.570 1.~15 . _ ~ ._ _ . . _ . _ .. _ .. . . . _ . .. .. . _ 19 128.031 4,210 41 _57,07Q__ _ 5~
__ __ ._~ ___. _ . _ _ 28.106 2.486 42 6~.251 2.720 . _ _ _ _ _._._ .. _ .. __ .____ __ ~
21 28. l 30 5.219 l~3 61.524 l~ .408 ~ _ ~_ _ ._.___~_ 22 29.610 1.015 44 62.52() 1.015 _ _____ _._.__ ______ ___ _ _,_ __________ ` - - - - . .. _ ~LS~'75i~
-3:L-TARl~E MO. 21 _ ¦ C_~ ~ .02 ¦ A + .015 ,, I . i - ..
45` 63.112 3.632 6~3 1 97.8:30 5.219 __ _ __. - .
46 63.430 1.874 69 1 99.95() 2.(171 __ _ .. ___ _ __ ___ .~ . _ . ._ ~
47 66.885 3.011 70 1~0.497 4.2~3 __ __ , ._ ___ ____.___ . __ _.____ e~
48 67.260 S~ 21g ~ I 10~ . s(,n ~ ~ 5~.
_ _. _ __. _ _ 49 7U .200 1 ~ OlS 7~ 104.091 3.609 _ . _ . _ _ __.__ ___ 71.692 3.819 73 ~06.'390 5,21') . ... ___ . . .. - I , . _ ' Sl 71.8401.874 74 107.490 1.015 . _ _ ,, .. .
52 73.3132.809I 75 108.J5] 2.461 , 53 78.2605.219 76 112.123 4.115 _ _ . . ___ __ ____ ______.__ 54 78,375 3.230 77 112.~30 ~ .5~1~
. _ _. ._ .. _ _ ___ _______._ . __.__ __.___.___ ______.. :____.. _._ -78.610 1.015 78 113,99l~ 3.154 _ ___ ___ ___ ___ _ _ ___ . .
56 79.520 1.874 F-_7" 117. '3~0L .~l5 _ 57 ~ ~0.372 4.125 ` _ _80 _ l l 7.390 __ _5. .1 '3 __, 58 82,533 2.6~3 ~1 ll8. S6'3 2.3~3 . ._~. _ .~___ ._. _ ___ . . __. . __. . ___ . _ _ _ 5986.470 1.874 ~32 11'3.55'3 4.0~ ~
. ...... _ _ _ ... _ ___ _ .. _ ._ _ ._ __ . ._ .
87.629 3.684 83 12? . -30() l .581 61 87.750 __ 1.015 __84 __ 1~'3 7-/9 '3.'337 62 88.450 5.219 _ 85 ~ 26 137 ~ 2Sf~
, _____ __ ___:_ __ __ __ 63 90.068 2.805 _ _ ___~6 ~ ~) .6~)9 2. '352 __ 64 92.690 1.874 __ 137 l 27.23~ - 1. '.~IS

93.839 4.370 ~38 127,5~3~ 5. ) I ') ______._ .... _ . __ 66 194.454 3.510 ___ __ l3~ 6 '3.769 67 197.620 1.015 9() I 3~.170 ] .5~1 r . .. . . .. .. .. .. . .

V

75~

NO o~ + .02 A + 015 .. , _ . .
~4 1 ~66.4~9 ~.7]~
___ 133 752 2.846 __ _ . _ __: _ _ 115 ~ 7.82~ 1. ()15 92 136.696 2.075 _ ______ _ _ _____ _ ~__ __ _ _ _ _ 93 136.960 5.219 __ ~ ) I . ~7~ _ ~7 l6').~' ~,.223 94 ~ 137.100 1.015 ____ __ - - _ llX1 170.25j 3 354 95 137.424 4.387 _ __ _ _ . . . _ . .
_96 140.~348 --779 ____ l19173 6;() 5.219 ~ '01 174. ~ 2.769 '~7 141.096 3.760 __ __ ~ ______ _ __ ~-121176.2)() ~ 015 98 142.040 1 581 _ _____ ~r 99 145.436 4.405 1~2177. l4r) ] .X-/~
....... ___ __. ___ lQ0 145.520 5.219 123t- l78.358__ 3.737 . .__ ~ . ._.
101 146.970 1.015 12'I-32.~37~. 4.377 1251 ~3. 5~ 2.74 102 147.941 2.604 , , , ~_ _ _ .
103 , 149.654 3.648 126 1~34.090 ~.~74 .. .. __ _. _ _ ,__ ___ _. __ _ _ . _ 104 151.839 4 399 I27 18~....... 650 50219 _ __. _ ___ . ._. .__. .. _ ___ _ .... _ . .
105 151.910 1.874 ; 128 1~5.370 I.()l 5 _ ____... .__ .. _ _ .__. _ .__.. _ .. _. _ .. .......
106 153.190 1.015 l ~9 18~ 493 3 ~53 ___;......... _.. _ .. __. _. .. _.. '. __ . _.. ._.. _.. -............ ...
07 154.080 5.219 130 l~9.~37~ 2.81 f) _. ___ .____ ____ .___ _._ ._._ .. _ __.
108 ~53.089 4.054 13~ 1'30~ l.~74 __ . _ __ _ . _ . . __ _ . __ _ _. _ __ _ . . _ ___. ._.. _ _ _ . . _ 1091 158.699 3.026 132 193 2l0 5.'1~

___ _ r 110 160.140 _ 1.015 : I'~ '~ .32~ '~ .332 111 161.050 1.874 13~1 l95.240 1.01, _._._ .___ _ _ . _ ___.____ ____ _ ____ 112 ~63.460 5.219 135 1'~5.86'3 3.329 _ ___.__. .______._~ ._.. _ ._ ________. _ __ _. _____ .__._____ 113 164.354 3.560 136 196.470 2.543 _ .__ __ __ . . _ _ _ . _ _ __ . __ ~4'7~

TABLE N0. 2 I I o N0 c~ + .02 ~ + .015 . _ ~= __ I _ _ 137 200.180 1.581 160 L23~.... 720 1.0~5 .___ _ ._ _ . __ _ --~ -- 1- ---------------161 2,6 r) I ~ 3.715 138 2~1; J'l5 3. ~17 __ _ _ _ __ _ _ _ ___ __ .. . ____ _ _.
162 239.660 1.5~1 139 202.590 ___ __ _ _ _ __ ___ _ _ ___ _ ____ _ 163 1 _:39,~1# 2,5~5 1401 203.419 2.736 - t- ~_ _ i64 1 2~3.279 3.860 141. 205 110 __ 1.015 __ _ _ _ _ __ _ _ _ _ __ ___ ~65 1 243.350 5.219 142207.630 3.636 _ - ___ _ .. __ ______ 143210.050 1.58116() ' 2~l~i.590 1.01;
__ ___ __ . .. .. _ .. _ .. __ _ _ _ _ .. . _ _ . h ] f~7 ~ 2~1f~ .4f~5 3.013 144210.6~0 _4 386 _ _ ._______ 145212.7805.219 16~3 ~3. ~'J3 4.408 _ _ __ 146213.4092.565 _ I169 1~19.530 1. ~37~
17~ 250. U l~ l .O~ S
14721409801.015 _ _ _ ____ __ _ _ ____ __ __ _ I_ 171 '~51.9~() 5.219 148216.6323,419 _ _~ r 149. 219.5914 121 172 1 252.289 3.68~
` ......... _ .... I .. __.. __ ....... _ ___ 150219.9201.58~ l ] 7 ~ 25~ 357 2, f~3~
~_____ ______ _ _ __-----f , 174 255`2'~5 4.~06 151222.127 _ 2.31 L __ ' ____ ___ __ ______________ 152223.780 5.219 175 257.760 1.01~
. _ I _ . . .
153224.850 1.015 176 258.377 3.700 _ _ __ ._ _______ 177 258.670 1. ~37 154226.714 3.432 __ _._____ _ _. ._ __. _.____. .
155~27.463 4.334 178 26] .421 2.940 .~ ___ __ ___ _.___ ._._. ._ 156 227.869 2.47fi 179 262~6~l 4.393 ~_ ____ _ __ __ . _ . _ _ _ _ . .. . _ _ . _ . _ _._ .. ._ . .. _ .. . . .. .
157 229.79~ ] .581 18U 262.~10 5.21'J
_ __ _ _____ _______ ___.__ 233.891 2.523 ______ 265.440 ___ 1.()15 _ 159 1 233,970 1 5.219 __1s~ )7.()~() 1.8/~

11_ --- - __ .
.

~15~752 . ` -34--TABLE N0. 2 _ _ NOCYC t 2 A -~ 015 . _ . ............... . I i 2l)() 1~()2 7~0 1 ~L5 183267.480 2.973 __ __ ' . r-. . . ___ ~
207 303 5~l3 2 273 184268.016 3.855 _ __ _ __ __ _ __ .__ .. _ 208 303.757 3.214 185273.100 5,219 _ __ _ 2()9 307.670 1,581 186273. B50 I,015 ' _ _ . _ ____ _ 187274,244 3,717 'lO ¦ 30R,371 3,97Y p_ _ _ . _ 211 30~3. ')80 S .219 188274.277 2.675 _ _ _ _ _ ___ ______ ._ __ . .
j 18g~7~ " ~ 0 1,874 2 L2 3 L ',392 2. L73 .__ _. ...........
213 312.600 1,015 190 281,37 l ~,179 _ __ _____ _ _._ .. ... ..
L91 281.7L0 1.87~ ~I4-_ 312,~) _~ 6 192 282,~80 5,219 215L316.4t)C _ _3. -~97 _ 193 282.990 1,0]5 '1~ 31~,5~ 1,'~1 . _ . .... .... __ .. . .... . . .. . .... _ 217319.0hl 2,857 194 283,177 3,063 ___I__ ____ _ r _ __ _ l 195 286.821 3.747 21~ 319,170 5.219 196 287,930 1,874 219 1 322,471~ 1.015 ..... ~ _ .. __. _ ___. __ ' 197 290,555 2,745 , 22() 322.952 4,062 . 221 324,~l49 2~ 7 198 291 040 5.219 ______________ . . _ _ 199 291.477 ' 4.276 222 326~ 3~t3 3,367 200 292,860 1,015 223 32i,410 1,581 ___. --- ~ L, .
201 296.741 2.788 22~ 330.17() j 5.2~ 9 225 330.372 4.017 ~-202 297.799 3.720 l__ . ._. .___ 203 297,800 1.581 226 331, l9'~ 2.40/3 I . _ ___ . ._.____ . ___ _ . .
204 299.600 5.219 22 ~ 332, ~ ) 1, ~15 __ ______ _ __ .. _ _ _ __ . __ _ __._.. __ .
205 301,114 4,381 2 '~, 332,482 3. ~
__ . . .___ , _ _ . ___ __ _._ _ ,___ . .. ... . .. .

. .
`:

.

~i54'7~

TA]3L~ NO. 2 _ . _ ., , ~ . . .. .. . ....................... _ .

N0 Lo~ -~ .02 ~_ _ _ ____ L~9 33~,16~ ll,3')~
~ . . _._ _._.___ . _ ~. . . _ '30 137.2~() 1 5)3l ~31 _~_.333 _ ~ 7~__ 232 338.730 ~ .219 _ . __ _ _ _ ~ _ V--233 339.433 _ - 9 234 342,210 1,015 . ' ~. __ ____,_ 235 342 237 2,()15 236 342,684 4, L~i3 ~-_ _ ~
237 346,008 2, fi')0 _. _~ _ __ . : _ __ .__. _.. .. .. .. ._ ..
238 346,570 3,54~
___ _ __. _ _ ~39 347,150 ~,5~1 _ 240 348,110 5, ? 19 _ _ __ . _ __ _ ___ .. ..
2~ 3~9, C~0 _ _ _,307 242 352,08(~ i .015 __ __ __ _~
243_ 353.573 1.~3~7 .4435~,114 ___ 3 010 _ 245357,263 3, ~35C !
_ _ ~ L
24fi - 358,741- ~

5~

Claims (10)

The embodiments of the invention in which an exclusive property or privilege is claimed are defined as follows:

1. In an earth boring bit having a cutter shell rotatably mounted on the bit, the shell having a gage region on its outer side and an intermediate region joining the gage region and extending inwardly, an improved cutting structure comprising in combination:
first and second staggered rows of cutting elements located in the intermediate region.
a plurality of cutting elements located in a pattern in the intermediate region free of all types of rows.

2. The drill bit according to claim 1 wherein the cutting elements are located at different distances from each other and at different distances from the gage region of the cutter.

3. The drill bit according to claim 1 wherein the cutting elements are identifiable in sets of three adjacent cutting elements which are located relative to each other in a spacing that differs from the spacings of all of the other sets.

4. The drill bit according to claim 1 wherein each cutting element has a surrounding boundary zone with minimum and maximum desired distances between any two of the cutting elements, and wherein each of the cutting elements within the pattern is randomly located within one of the boundary zones of another of the cutting elements.

5. The drill bit according to claim 1 wherein all of the cutting elements in the pattern are randomly located outside of minimum boundary zones surrounding each cutting element.

6. The drill bit according to claim 1 wherein the intermediate region contains a circumferential heel row of cutting elements located next to the gage region, with the pattern being located inward from the heel row.

7. The drill bit according to claim 1 wherein the cutter has a nose region on its inner side, separated from the gage region by the intermediate region, and wherein the intermediate region has a circumferential row of cutting elements located near the gage region, and the nose region also has a circumferential row of cutting elements, with the pattern being located between the rows.

8. The drill bit according to claim 1 wherein the cutting elements are located by the following method:
defining for each cutting element in the pattern a surrounding boundary zone that has an inner boundary corresponding to the minimum desired distance between the cutting elements, and an outer boundary corresponding to the maximum desired distance between the cutting element;
arbitrarily selecting a location of a first cutting element;
randomly selecting the location of a second cutting element within the first cutting element's boundary zone;
randomly selecting the location of a third cutting element within the second cutting element's boundary zone, and outside the inner boundary of the first cutting element; then randomly selecting the location of each succeeding cutting element within the boundary zone of the preceding cutting element and outside the inner boundaries of the preceding cutting elements.

9. For an earth boring drill bit, an improved cutter comprising:
a cutter shell rotatably mounted on the drill bit, the shell having a nose region on its inner side and a gage region on its outer side separated by an intermediate region;
a circumferential heel row of inserts located in the intermediate region next to the gage region;
first and second staggered rows of inserts located in the intermediate region next to the heel row inserts, with the second staggered row being located farther from the heel row that the first row by an amount less that the diameter of any of the inserts of the first and second staggered rows;
the first and second staggered rows of inserts being positioned in groups containing a plurality of inserts, the groups of each row being circumferentially spaced apart and alternated so that a group of the second staggered row follows a group of the first staggered row; and a plurality of irregularly located cutting elements comprising inserts positioned in the intermediate region bounded on the outer side by the first and second staggered rows of inserts, each insert in the intermediate region having a surrounding boundary zone with minimum and-maximum distances between centerlines of any two inserts;
substantially all of the irregularly located inserts being randomly located within one of the boundary zones of another of the irregularly located inserts and in a pattern that is free of all types of rows.

10. An earth boring drill bit for boring shafts comprising in combination:
a cutter support member adapted to be connected to a string of drill pipe for imparting rotary drive to the cutter support member;
at least one inner cutter rotatably mounted to the cutter support member adjacent the center of the cutter support member for disintegrating the earth formation face in the vicinity of the center of the shaft;
a plurality of gage cutters rotatably mounted at the periphery of the cutter support member for disintegrating the earth formation face in the gage vicinity; and a plurality of intermediate cutters rotatably mounted to the cutter support member between the inner cutter and the gage cutters at regular intervals for disintegrating the earth formation face in the vicinity between the center and the gage areas:

the intermediate cutters having a plurality of cutting elements located in an insert pattern free of all types of rows;
the gage cutter having a nose region and a gage region separated by an intermediate region, and a plurality of cutting elements located in an insert pattern of hard metal inserts comprising:
first and second staggered rows of inserts located in the intermediate region, the first and second staggered rows being positioned in sets of at least one insert, the sets of each staggered row being circumferentially spaced apart and alternated so that a set of the second staggered row follows a set of the first staggered row; and a plurality of irregularly located inserts positioned in the intermediate region bounded on one side by the first and second staggered rows, each irregularly located insert being located in a pattern free of rows.